What is the domain of the function f(x) = √(x+3)²?

The coordinates of the vertex of the parabola are (-6,5).

The coordinates of a vertex of a parabolic equation are those x and y points for which the parabola crosses its axis of symmetry.

The vertex of an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

[tex]\mathbf{x_v = -\dfrac{2}{2(1/6)}}[/tex]

[tex]\mathbf{x_v = -6}[/tex]

From the equation:

[tex]\mathbf{y = \dfrac{1}{6}x^2+2x+11}[/tex]

[tex]\mathbf{y_v = \dfrac{1}{6}(-6)^2+2(-6)+11}[/tex]

[tex]\mathbf{y_v =5}[/tex]

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Answer:

[tex]-\dfrac{463}{7}[/tex]

Explanation:

Given equation: 2x² - 6x - 7 = 0

In quadratic equation: ax² + bx + c

[tex]Sum \ of \ roots : \alpha + \beta = \dfrac{-b}{a}[/tex]

[tex]product \ of \ roots : \alpha \beta = \dfrac{c}{a}[/tex]

So, here given:

[tex]Sum : \alpha + \beta = \dfrac{-(-6)}{2} = 3[/tex]

[tex]Product : \alpha \beta = \dfrac{-7}{2} = - 3.5[/tex]

For finding value:

[tex]\dfrac{\alpha^3}{\beta } + \dfrac{\beta^3 }{\alpha }[/tex]

join fractions

[tex]\dfrac{\alpha^4+ \beta^4}{\alpha \beta }[/tex]

factor out

[tex]\dfrac{(\alpha^2 + \beta ^2)^2 -2\alpha ^2 \beta ^2 }{\alpha \beta }[/tex]

when factored more

[tex]\dfrac{((\alpha + \beta)^2 -2\alpha \beta )^2 -2(\alpha \beta)^2 }{\alpha \beta }[/tex]

insert values inside

[tex]\dfrac{((3)^2 -2(-3.5) )^2 -2(-3.5)^2 }{-3.5 }[/tex]

calculate for value

[tex]-\dfrac{463}{7}[/tex]

Sam paid $ 124.032 as tax deduction each week.

An equation is a mathematical statement formed when an algebraic expression is equated by an equal sign by a constant or algebraic expression.

It is given that

weekly earnings of Sam is $912

Tax deduction is 13.6 %

Let the amount of Tax deduction is represented by $x

Then the equation formed is

x = 13.6 % 912

x = 13.6 *912 /100

x = $ 124.032

Therefore Sam paid $ 124.032 as tax deduction each week.

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The value of x is 4.

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given:

In ΔCDB and ΔEAB

<CDB = <ABE    (alternate interior angle)

<DBC = <EAB    (alternate interior angle)

By AA similarity criteria

ΔCBD ~ ΔEAB

Now,

EB/ CD= EA/CB

6/x-1 = 4/x-2

6X-12= 4X-4

2x= 8

x=4

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Answer:

  $7800

Step-by-step explanation:

The total interest earned can be found by summing the earnings from each of the investments.

Let x represent the total amount invested. Then Jessica's earnings are ...

  (x/2)(0.07) +(x/2)(0.13) = 780

Simplifying the equation gives ...

  (x/2)(0.07 +0.13) = 780

  0.10x = 780

  x = 7800 . . . . . . . . divide by 0.10

Jessica has $7800 invested.

Answer: -10x+1.5

Step-by-step explanation:

[tex]-2(5x-0.75)=-10x+1.5[/tex]

Answer:

b

Step-by-step explanation:

Answer:

the answer is 3power 7

3^7

Answer:

3^8

Step-by-step explanation:

Evaluating the function in x = -1, we get:

H(-1) = 7

When we have a function:

y = f(x)

Evaluating the function in a value, like x = a gives:

y = f(a).

This means that we need to replace all the "x" in the equation by the number "a".

In this case:

H(x) = 6 - x

And we want to get:

H(-1)

So we need to replace the x by -1.

H(-1) = 6 - (-1) = 7

H(-1) = 7

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Step-by-step explanation:

[tex]( \sec(x) + \tan(x) )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex]( \frac{1}{ \cos(x) } + \frac{ \sin(x) }{ \cos(x) } )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex]( \frac{1 + \sin(x) }{ \cos(x) } )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex] \frac{1 - \sin {}^{2} (x) }{ \cos {}^{2} (x) } [/tex]

[tex] \frac{ \cos {}^{2} (x) }{ \cos {}^{2} (x) } [/tex]

[tex] = 1[/tex]

It is false that x is a function of y

The equation is given as:

x = y^2

Set y = 2

x = (2)^2

x = 4

Set y = -2

x = (-2)^2

x = 4

Different values of y give the same x value.

This means that x is not a function of y

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The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The given triangle can be solved as shown below.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

For the given triangle, using the sine rule the ratio of the angle and the sides of the triangle can be written as,

[tex]\dfrac{Sin\ A}{18} =\dfrac{Sin\ B}{11} =\dfrac{Sin\ C}{c}\\\\\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ y^o}{11} =\dfrac{Sin\ x^o}{c}[/tex]

Taking the first two ratios,

[tex]\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ y^o}{11}\\\\y = 35.54^o[/tex]

The sum of all the angles of a triangle is 180°.

72° + 35.54° + x° = 180°

x = 72.46°

Now, using the sine ratio,

[tex]\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ 72.46^o}{c}\\\\c = 18.046[/tex]

Hence, the given triangle is solved.

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Thoughts:  The best that I was able to do was simplify it in this form.

Answer:    V    

Her boss would give Kim a total of $2x

The given parameters are:

Distance = 26 km

Assume that the amount raised during the marathon is

Amount = x

From the question, we have:

Boss = Double the amount

This means that:

Boss = 2 * Amount

Substitute Amount = x

Boss = 2x

Hence, her boss would give Kim a total of $2x

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The x-intercepts of the parabola are (3, 0) and (7,0)

The given parameters are:

Vertex (h, k) = (5, -12)

Point (x, y) = (0, 63)

The equation of a parabola is:

y = a(x - h)^2 + k

Substitute (h, k) = (5, -12)

y = a(x - 5)^2 - 12

Substitute (x, y) = (0, 63)

63 = a(0 - 5)^2 - 12

Evaluate

63 = 25a - 12

Add 12 to both sides

25a = 75

Divide by 26

a = 3

Substitute a = 3 in y = a(x - 5)^2 - 12

y = 3(x - 5)^2 - 12

Set y to 0 to determine the x-intercepts

0 = 3(x - 5)^2 - 12

Add 12 to both sides

3(x - 5)^2 = 12

Divide by 3

(x - 5)^2 = 4

Take the square root of both sides

[tex]x - 5 = \pm 2[/tex]

Add 5 to both sides

[tex]x = 5 \pm 2[/tex]

Expand

x = (5 - 2, 5 + 2)

Evaluate

x = (3, 7)

Hence, the x-intercepts of the parabola are (3, 0) and (7,0)

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Answer:

(a)  5165.42 rupees

(b)  $1.35

Step-by-step explanation:

Given information:

Part (a)

To find how many rupees $103.64 was worth, multiply the number of dollars by the number of rupees per dollar:

⇒ 103.64 × 49.84 = 5165.42 rupees (nearest hundredth)

Part (b)

To find how many dollars 67.36 rupees was worth, divide the number of rupees by the number of rupees per dollar:

⇒ 67.36 ÷ 49.84 = $1.35 (nearest hundredth)

Answer:

Step-by-step explanation:

[tex]\frac{a+b}{a^2b} +\frac{a-b}{ab^2} \\=\frac{b(a+b)+a(a-b)}{a^2b^2} \\=\frac{ab+b^2+a^2-ab}{a^2b^2} \\=\frac{b^2+a^2}{a^2b^2} \\or\\=\frac{1}{a^2} +\frac{1}{b^2}[/tex]

[<Answer>] (1):
Heyy there, it's Avery. And I'm here to help! :)

----------------------------------------------------------------------------------------------------------[<The Explanation>]:

Let x= number of watches sold

Ethan= x(14) + (20)(1.50)

Roy = x(13.50) + (20)(1.80)

Since they collected the same amount of money:

14x + (20)(1.50) = 13.50x + (20)(1.80)

Combine like terms:

14x - 13.50x = (20)(1.80) - (20)(1.50)

0.50x = 36 - 30

0.50x = 6

x = 6/0.50

x= 12

Ethan sold 12 watches. And also Roy.
Andddd...We're done! :D

----------------------------------------------------------------------------------------------------------
[<Ending>] <3

Hope this helps and if it's wrong, you can't sue me! :D

Bye! Hope this works for you :)

Have a nice day! - Avery <3

The equation that can be used for finding the lengths in the Pythagoras theorem include:

b² = c² - a²

a² = c² - b²

c² = a² + b²

It should be noted that a Pythagoras theorem is simply the theorem that's used in finding the missing length of a right angled triangle.

In this case, the equation that can be used to find the sides in a Pythagoras theorem has been given.

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Answer:

He have to invest $527.777778 .

Step-by-step explanation:

X : 4.75% = $10,000 : 90

Answer:

The volume = 5 276.66928645188 cm³

Step-by-step explanation:

let V be the volume of the given sphere.

V = (4/3)×π×r³ ,where r is the radius of the sphere

r = 21.6÷2 = 10.8 cm

Then

V = (4÷3)×π×(10.8)³

   = 5 276.66928645188 cm³

The algebraic expression is:

x + (2x - 11) = 13

And the solution is x = 8.

Let's say that the number is defined by the variable x, then we can write the algebraic expression:

x + (2x - 11) = 13

Now we can solve this expression for x:

x + 2x - 11 = 13

3x = 13 + 11 = 24

x = 24/3 = 8

x = 8

The solution is x equal to 8.

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Answer:

  (a)  (5, -3)

Step-by-step explanation:

The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.

The given equations are ...

We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.

When the expression (x-8) is substituted for y in the second equation, you get ...

  2x +3(x -8) = 1

This simplifies to ...

  5x -24 = 1

This 2-step equation can now be solved in the usual way:

  5x = 25 . . . . . . add 24 to isolate the variable term

  x = 25/5 = 5 . . . . . divide by the coefficient of x

Note that we now know what the correct answer choice is.

Using the expression for y, we find ...

  y = x -8 = 5 -8 = -3

The solution is (x, y) = (5, -3).

__

The attached graph confirms this solution.

Answer:

4

Step-by-step explanation:

When we substitute the blank for 4 and divide by 4, 7,504,124/4 is 1,876,031 :)

Have an amazing day!!

Please rate and mark brainiest!!

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by elimination.

x−3y=9;−x+3y=−9

x−3y=9

−x+3y=−9

Add these equations to eliminate x:

0=0

Answer:

Infinitely many solutions.

Answer:

3081.24 cm³ (nearest hundredth)

Step-by-step explanation:

Formulas

[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

If a rectangular piece of paper is rolled along its length to form a cylinder:

To calculate the volume of the formed cylinder, determine the radius by using the circumference formula:

[tex]\implies \sf 2 \pi r = 44[/tex]

[tex]\implies \sf r = \dfrac{44}{2 \pi}[/tex]

[tex]\implies \sf r =\dfrac{22}{\pi}[/tex]

Substitute the round radius into the formula for Volume and solve for V:

[tex]\implies \sf V=\pi \left(\dfrac{22}{\pi}\right)^2(20)[/tex]

[tex]\implies \sf V=\pi \left(\dfrac{484}{\pi^2}\right)(20)[/tex]

[tex]\implies \sf V=\left(\dfrac{484}{\pi}\right)(20)[/tex]

[tex]\implies \sf V=\dfrac{9680}{\pi}[/tex]

[tex]\implies \sf V=3081.239698...cm^3[/tex]

Therefore, the volume of the cylinder is 3081.24 cm³ (nearest hundredth).

Answer:

You can find the mean, by adding all the terms in each data set and dividing by the number of terms.  For example, if there were four data points, you would add them all up and divide by four.

hope this helps!

Answer:

[tex]3x^{2} +2x[/tex]

Step-by-step explanation:

Using the rainbow expansion method:

[tex]x(3x+2)=3x*x+x*2\\ = 3x^{2} +2x[/tex]

Answer:

3x² + 2x

Step-by-step explanation:

x (3x + 2)

= x*3x + x*2

= 3x² + 2x

Answer:

about x=38.1

Step-by-step explanation:

9x38.1=342.9

Step-by-step explanation:

[tex] \log(x) = - 1[/tex]

[tex] \log(y) = 6[/tex]

[tex] \log(z) = 2[/tex]

[tex] \: [/tex]

[tex] = \log( \frac{ {x}^{3}y }{ {z}^{2} } )[/tex]

[tex] = \log( {x}^{3} \times y \div {z}^{2} )[/tex]

[tex] = \log( {x}^{3} ) + \log(y) - \log( {z}^{2} )[/tex]

[tex] = 3 \log(x) + \log(y) - 2 \log(z)[/tex]

[tex] = 3.( - 1) + 6 - 2[/tex]

[tex] = - 3 + 6 - 2[/tex]

[tex] = 1[/tex]